Study of New Class of q-fractional Derivative Operator and its Properties

Abstract

There are several approaches to the fractional differential operators.Generalized q-fractional integral operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. In the following paper, we introduce the Caputo type derivative related to the mentioned operator and some properties of this operator is investigated.  Cauchy problem based on this operator is studied and existence and uniqueness is discussed.